Your ""refutation"" overlooks an important distinction:
what people think about a social practise
versus
what is actually the case about a social practise.
Example: in the U.S. South in the early 19th century,
most people thought slavery was a desirable institution,
and that African people were innately inferior to Europeans,
and provided by Divine Providence to pick cotton for their masters.
However, this belief was false, even though most people believed it.
The few who opposed it, even at the cost of being mocked and
vilified, were right.
Two different social beliefs.
The majority, wrong.
A minority, right.
Another familiar example is the general belief by
German people in 1933-1945 that they were a ""Herrenvolk""
and should do as they wished with other ethnic groups.
Again, there was a persecuted minority that
disagreed. But the majority were wrong, the minority right.
(In other cases, of course, the majority may be right.)
When I say that a distinctive feature of mathematics is
the high consensus obtained among it practitioners, I
am not saying that the high consensus is what makes
a correct mathematical theorem correct. I am saying
that the attainment consistently of this consensus
is the visible evidence that mathematical correctness
"exists."
Please don't misunderstand again!! I am not saying
that ""philosophical"" questions, about
math or anything else, are comparable in importance
to slavery or genocide. I am using dramatic
examples in the hope of conveying the point.
Majority belief on a social question is not identical to the truth
about that social question.
The tone of your ""posting"" suggests a belief that
my issue about the nature of mathematical reality is of
little or no interest to you. Do you then ""refute""
your lack of interest by taking the trouble to ""refute"" me?
Try again, refuting your ""refutations"" is fun.
Hersh